3,661 research outputs found
Concentration inequalities for mean field particle models
This article is concerned with the fluctuations and the concentration
properties of a general class of discrete generation and mean field particle
interpretations of nonlinear measure valued processes. We combine an original
stochastic perturbation analysis with a concentration analysis for triangular
arrays of conditionally independent random sequences, which may be of
independent interest. Under some additional stability properties of the
limiting measure valued processes, uniform concentration properties, with
respect to the time parameter, are also derived. The concentration inequalities
presented here generalize the classical Hoeffding, Bernstein and Bennett
inequalities for independent random sequences to interacting particle systems,
yielding very new results for this class of models. We illustrate these results
in the context of McKean-Vlasov-type diffusion models, McKean collision-type
models of gases and of a class of Feynman-Kac distribution flows arising in
stochastic engineering sciences and in molecular chemistry.Comment: Published in at http://dx.doi.org/10.1214/10-AAP716 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Global existence results for nonlinear Schrodinger equations with quadratic potentials
We prove that no finite time blow up can occur for nonlinear Schroedinger
equations with quadratic potentials, provided that the potential has a
sufficiently strong repulsive component. This is not obvious in general, since
the energy associated to the linear equation is not positive. The proof relies
essentially on two arguments: global in time Strichartz estimates, and a
refined analysis of the linear equation, which makes it possible to use
continuity arguments and to control the nonlinear effects.Comment: Some typos fixed, Proposition 1.1 extended. Final version to appear
in DCD
One more approach to the convergence of the empirical process to the Brownian bridge
A theorem of Donsker asserts that the empirical process converges in
distribution to the Brownian bridge. The aim of this paper is to provide a new
and simple proof of this fact
Representations of stack triangulations in the plane
Stack triangulations appear as natural objects when defining an increasing
family of triangulations by successive additions of vertices. We consider two
different probability distributions for such objects. We represent, or "draw"
these random stack triangulations in the plane and study the asymptotic
properties of these drawings, viewed as random compact metric spaces. We also
look at the occupation measure of the vertices, and show that for these two
distributions it converges to some random limit measure.Comment: 29 pages, 13 figure
Generalizing Consistency and other Constraint Properties to Quantified Constraints
Quantified constraints and Quantified Boolean Formulae are typically much
more difficult to reason with than classical constraints, because quantifier
alternation makes the usual notion of solution inappropriate. As a consequence,
basic properties of Constraint Satisfaction Problems (CSP), such as consistency
or substitutability, are not completely understood in the quantified case.
These properties are important because they are the basis of most of the
reasoning methods used to solve classical (existentially quantified)
constraints, and one would like to benefit from similar reasoning methods in
the resolution of quantified constraints. In this paper, we show that most of
the properties that are used by solvers for CSP can be generalized to
quantified CSP. This requires a re-thinking of a number of basic concepts; in
particular, we propose a notion of outcome that generalizes the classical
notion of solution and on which all definitions are based. We propose a
systematic study of the relations which hold between these properties, as well
as complexity results regarding the decision of these properties. Finally, and
since these problems are typically intractable, we generalize the approach used
in CSP and propose weaker, easier to check notions based on locality, which
allow to detect these properties incompletely but in polynomial time
Loti ve eserleri
Taha Toros ArĆivi, Dosya Adı: Pierre LotiÄ°stanbul Kalkınma Ajansı (TR10/14/YEN/0033) Ä°stanbul Development Agency (TR10/14/YEN/0033
Living a Lie: Why Don\u27t Ask Don\u27t Tell Presents an Unworkable View of Personhood
A fundamental conflict exists between the understanding of personhood in asylum law and its conception in military law. Asylum law in the United States and the United Kingdom recognizes homosexuality as a fundamental characteristic of personhood, which cannot be concealed. Conversely, âDonât Ask Donât Tell,â the statutory ban on gays serving openly in the U.S. Military, demands complete suppression of any indication of homosexuality. This Comment argues that, in light of the framework for examining personhood most recently articulated by the U.K. Supreme Court, the arguments in favor of âDonât Ask Donât Tellâ are both specious and destructive. This Comment proceeds first by examining the understanding of personhood in asylum law. It then contrasts this understanding with the demands and restrictions that âDonât Ask Donât Tellâ imposes on homosexual military personnel. Finally, this Comment concludes by calling for a uniform application of the view of personhood found in asylum law
Multi-Armed Bandits for Intelligent Tutoring Systems
We present an approach to Intelligent Tutoring Systems which adaptively
personalizes sequences of learning activities to maximize skills acquired by
students, taking into account the limited time and motivational resources. At a
given point in time, the system proposes to the students the activity which
makes them progress faster. We introduce two algorithms that rely on the
empirical estimation of the learning progress, RiARiT that uses information
about the difficulty of each exercise and ZPDES that uses much less knowledge
about the problem.
The system is based on the combination of three approaches. First, it
leverages recent models of intrinsically motivated learning by transposing them
to active teaching, relying on empirical estimation of learning progress
provided by specific activities to particular students. Second, it uses
state-of-the-art Multi-Arm Bandit (MAB) techniques to efficiently manage the
exploration/exploitation challenge of this optimization process. Third, it
leverages expert knowledge to constrain and bootstrap initial exploration of
the MAB, while requiring only coarse guidance information of the expert and
allowing the system to deal with didactic gaps in its knowledge. The system is
evaluated in a scenario where 7-8 year old schoolchildren learn how to
decompose numbers while manipulating money. Systematic experiments are
presented with simulated students, followed by results of a user study across a
population of 400 school children
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